WASHINGTON — The Senate, in a predawn vote two hours after the deadline passed to avert automatic tax increases, overwhelmingly approved legislation on Tuesday that would allow tax rates to rise only on affluent Americans while temporarily suspending sweeping, across-the-board spending cuts.

The deal, worked out in furious negotiations between Vice President Joseph R. Biden Jr. and the Republican Senate leader, Mitch McConnell, passed 89 to 8, with just three Democrats and five Republicans voting no. Although it lost the support of some of the Senate’s most conservative members, the broad coalition that pushed the accord across the finish line could portend swift House passage as early as New Year’s Day.

Many Democrats are unhappy about some of the provisions in the legislation (that’s why it’s called a “compromise”) but make no mistake — breaking the back of the anti-tax right wing is an historic achievement for the Obama administration.